The first coronavirus case in the South Island is a Danish tourist aged in her 30s who had visited a Queenstown adventure attraction and restaurant before seeking medical help.

The woman had travelled from Denmark and arrived in Auckland via Doha on flight QR 920 on Tuesday March 10, Director-General of Health Ashley Bloomfield confirmed today.

She then flew from Auckland to Christchurch on Jetstar flight JQ225, arriving at 8am on March 10.

The woman travelled to Queenstown by private rental vehicle.

The woman was unwell and hospitalised for one night. She is now recovering well and has been discharged. She will recover in self-isolation and will be monitored daily by health officials.

The Otago Daily Times reported that the woman checked into a holiday park near Queenstown's town centre.

The woman's group did an adventure activity on Thursday and ate at a resort restaurant that evening, when the woman began feeling unwell.

She visited Queenstown Medical Centre's Isle St clinic, without ringing ahead, either that evening or on Friday morning and was informed of the positive test yesterday.

After the Southern District Health Board told the Queenstown Lakes District Council of the positive result, the woman and at least one companion spent Saturday night in the Queenstown Events Centre car park, where they remained until about noon today.

The woman is now believed to be in isolation in the camper van at the council's camping hub in Frankton, which has been closed to other campers.

The ODT reported that the woman ate at a second downtown restaurant on Friday, and was possibly using shared facilities at the holiday park during the three nights she stayed there.

The seventh case was an Australian man in Wellington, who came from Australia and has tested positive. He arrived at 12.05am yesterday morning from Brisbane on Air NZ flight 828.

He was self-isolating with his partner and another family member, and was symptom-free. He does not need hospital treatment.

Contact tracing on the flights the seventh and eighth cases traveleld to New Zealand on has been changed to two seats in all directions: front, back, both sides and diagonal. This is supported by current evidence and is in line with the same approach taken by European authorities.

In both instances public health staff are conducting contact tracing and requesting close contacts stay in self isolation for 14 days from the date of potential exposure.

Healthline knows the seat numbers and will be able to advise anyone on the flight, whether they are considered a close or casual contact.

The fact that these two more confirmed cases had travelled from overseas reinforced the importance of the new travel restrictions, announced yesterday, for all people coming to New Zealand to self-isolate for 14 days - which kicks in at 1am tonight.

All previous confirmed cases have now recovered or are recovering at home, Bloomfield said.

Three people have also been isolated on a cruise ship in Akaroa, and are being tested. Two of them were in close contact with a previously confirmed case, one of whom had symptoms.

All on board are not allowed off the ship until those test results are known, he said.

Bloomfield thanked the New Zealanders who had been through self-isolation in the last four to six weeks, and work is underway to "scale-up" the response as the number of people in self-isolation is expected to ramp up.

The only infections in New Zealand were within family members, he said.

Latest studies showed that people can be infectious in the early stages of getting Covid-19, he said, and the most common way of getting infected was being in repeated close contact with someone who had it.

That reinforced the importance of staying at home if you're feeling unwell, he said.

That would allow the health system to be able to cope with the number of cases as they came up, he said.

People on the same flights as the seventh and eighth cases should contact Healthline - 0800 358 5453 - to see if they were in close contact with the positive cases.

The DHB was looking at how to manage its staff, including vulnerable staff, as well as setting up community-based clinics, which should be ready by Wednesday.

Testing capacity would also be ramped up, including two shifts of staff on from tomorrow, so that testing could take place twice a day.